Final Activity Report Summary - COMBIKNOT (Combinatorial knot theory) The project was concerned with knot theory, studying topological features of closed curves in three-dimensional space that were treated as rather stretchable pieces of physical rope. The focus was primarily combinatorial, with data about a curve being encoded in some finite symbolic sequence. The key problem was to achieve this in a way enabling to recognise when two encodings arose from different appearances of the same curve. % One major piece of work in this project was the development of techniques to handle the information originating from a controlled series of curve views, known as one-parameter knot theory, rather than from a standard single view. This was reported in the joint papers with Fiedler, and was used for further work by the time of the project completion. The project also developed algebraic techniques to simplify the analysis of combinatorial data arising in related areas. These included work on three-page embeddings of graphs, Gauss diagrams for links and link groups. Further algebraic results were achieved in establishing a compressed version of the Baker-Campbell-Hausdorff formula for Lie algebras.
